On a Matrix Model of Level Structure

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We generalize the dimensionally reduced Yang-Mills matrix model by adding d=1 Chern-Simons term and terms for a bosonic vector. The coefficient, κof the Chern-Simons term must be integer, and hence the level structure. We show at the bottom of the Yang-Mills potential, the low energy limit, only the linear motion is allowed for D0 particles. Namely all the particles align themselves on a single straight line subject to κ²/r² repulsive potential from each other. We argue the relevant brane configuration to be D0-branes in a D4 after κof D8's pass the system.